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Applications of Fixed Point Theorems for Multifunction to Integral Inclusions

In: An Introduction to Nonlinear Analysis and Fixed Point Theory

Author

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  • Hemant Kumar Pathak

    (Pandit Ravishankar Shukla University, School of Studies in Mathematics)

Abstract

Dynamical systems described by differential equations with continuous right-hand sides were the areas of vigorous steady in the later half of the twentieth century in applied mathematics, in particular, in the study of viscous fluid motion in a porous medium, propagation of light in an optically nonhomogeneous medium, determining the shape of a solid of revolution moving in a flow of gas with least resistance, etc. Euler’s equation plays a key role in dealing with the existence of the solution of such problems. On the other hand, Filippov, Differentsial’nye Uravneniya, 15:1814–1832, 1979, [232] has developed a solution concept for differential equations with a discontinuous right-hand side. In practice, such dynamical systems do arise and require analysis. Examples of such systems are mechanical systems with Coulomb friction modelled as a force proportional to the sign of a velocity, systems whose control laws have discontinuities.

Suggested Citation

  • Hemant Kumar Pathak, 2018. "Applications of Fixed Point Theorems for Multifunction to Integral Inclusions," Springer Books, in: An Introduction to Nonlinear Analysis and Fixed Point Theory, chapter 0, pages 765-791, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-8866-7_10
    DOI: 10.1007/978-981-10-8866-7_10
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